In a seminal work of Hayes [1]}, the \(\ell _2\) -Dobrushin's condition \(\Vert \rho \Vert _2<1\)  was proposed,
which has implications for several main approaches for mixing, e.g. coupling [1]}, spectral gap [3]}, log-Sobolev [4]} and modified log-Sobolev inequalities [5]}.
This condition was further generalizes by Dyer, Goldberg, and Jerrum in [6]} to arbitrary matrix norms.
